This is an interesting question!

Mosses belong to a group of plants known as the BRYOPHYTES. Bryophytes have no roots, but they do have thin (one cell thick!) root-like structures which serve for attachment and water absorption. These are known as RHIZOIDS.

Some kind of mosses or Bryophytes attach to the rocks by these rhizoids. Most mosses have very little resistance to drying out, and because most of the mosses are confined to areas which are damp and sheltered, some kind of rocks are suitable for them to live.

In Wales, for example, the majority of the rocks are acidic in nature, and this is reflected in may occur where the rocks are more base-rich (carboniferous limestone,for example). Once the rock has the natural conditions for the moss to grow(water, acid or basic nutrients), the moss is going to attach to the rock by means of the rhizoids.